Rotordynamic-Coefficients and Static (Equilibrium Loci and Leakage) Characteristics for Short, Laminar-flow Annular Seals

2005 ◽  
Vol 128 (2) ◽  
pp. 378-387 ◽  
Author(s):  
Dara W. Childs ◽  
Luis E. Rodriguez ◽  
Vito Cullotta ◽  
Adnan Al-Ghasem ◽  
Matthew Graviss
Keyword(s):  
Laminar Flow ◽  
Groove Depth ◽  
Test Results ◽  
Clearance Ratio ◽  
Industrial Practice ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Static Data ◽  
Deep Groove ◽  
Stiffness And Damping

Test results are presented for laminar-flow seals that are representative of buffered-flow oil seals in centrifugal compressors. The seals are short (L∕D≅0.21), with a diameter of 117mm and a clearance-to-radius ratio 0.0007. A smooth seal, a seal with one central groove, and a seal with three grooves were tested. Groove geometries employed are representative of industrial practice for compressors with a groove-depth to clearance ratio on the order of 6. Tests were conducted at 4000, 7000, and 10,000rpm shaft speed with delta pressures across the seals of 21, 45, and 69bars. For all cases, the flow was laminar. The seals were tested from a centered position out to an eccentricity ratio of 0.7. Static data included leakage and equilibrium loci for a range of loads. Direct and cross-coupled stiffness and damping coefficients and direct mass coefficients were determined from dynamic tests. For the smooth seal, comparisons between measurements and predictions were reasonable for the direct and cross-coupled stiffness and damping coefficients; however, measured added mass coefficients were roughly ten times larger than predicted. Predictions for the grooved seals from a “deep-groove” model that assumed zero pressure oscillations in the grooves greatly over predicted the influence of the grooves. In a centered position, smooth and grooved seals had comparable leakage performance. At higher eccentricity ratios, the grooved seals leaked modestly more. For eccentricity ratios less than approximately 0.3, the grooved seals and the smooth seal had qualitatively similar static and dynamic characteristics. In terms of cross-coupled stiffness coefficients, the grooved seals were less stable than the smooth seal at eccentricity ratios greater than approximately 0.5 but had significantly lower cross-coupled coefficients at reduced eccentricity ratios between zero and 0.3. A grooved centered seal is more stable than a smooth centered seal. The smooth seal had higher damping than the grooved seals and had moderately better centering capabilities.

scholarly journals Rotordynamic Coefficient and Leakage Test Results for Interlock and Tooth-on-Stator Labyrinth Seals

1988 ◽  
Author(s):  
Dara W. Childs ◽  
David A. Elrod ◽  
Keith Hale
Keyword(s):  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Test Results ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Leakage Test ◽  
Stiffness And Damping ◽  
Rotordynamic Coefficient

Test results (leakage and rotordynamic coefficients) are presented for an interlock and tooth-on-stator labyrinth seals. Tests were carried out with air at speeds out to 16,000 cpm and supply pressures up to 7.5 bars. The rotordynamic coefficients consist of direct and cross-coupled stiffness and damping coefficients. Damping-coefficient data have not previously been presented for interlock seals. The test results support the following conclusions: (a) The interlock seal leaks substantially less than labyrinth seals. (b) Destabilizing forces are lower for the interlock seal. (c) The labyrinth seal has substantially greater direct damping values than the interlock seal. A complete rotordynamics analysis is needed to determine which type of seal would yield the best stability predictions for a given turbomachinery unit.

Rotordynamic-Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals—Measurements Versus Predictions

2004 ◽  
Vol 126 (2) ◽  
pp. 326-333 ◽  
Author(s):  
Dara W. Childs ◽  
Jonathan Wade
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Test Results ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Static Data ◽  
Leakage Characteristics ◽  
Gas Seals ◽  
Stiffness And Damping ◽  
Rotordynamic Coefficient

Selected test results are presented for an annular gas seal using a smooth rotor and a hole-pattern-roughness stator for a supply pressure of 70 bar, three pressure ratios, three speeds up to 20,000 rpm, two clearances, and three preswirl ratios. Dynamic data include frequency-dependent direct and cross-coupled stiffness and damping coefficients. Static data include leakage and upstream and downstream pressures and temperatures. Very good agreements are found between measurements and predictions from a two-control-volume bulk-flow model.

scholarly journals Annular Honeycomb Seals: Test Results for Leakage and Rotordynamic Coefficients; Comparisons to Labyrinth and Smooth Configurations

1989 ◽  
Vol 111 (2) ◽  
pp. 293-300 ◽  
Author(s):  
D. Childs ◽  
D. Elrod ◽  
K. Hale
Keyword(s):  
Labyrinth Seal ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Shaft Rotation ◽  
Honeycomb Seal ◽  
Cell Dimensions ◽  
Honeycomb Seals ◽  
Rotordynamic Coefficient

Test results are presented for leakage and rotordynamic coefficients for seven honeycomb seals. All seals have the same radius, length, and clearance; however, the cell depths and diameters are varied. Rotordynamic data, which are presented, consist of the direct and cross-coupled stiffness coefficients and the direct damping coefficients. The rotordynamic-coefficient data show a considerable sensitivity to changes in cell dimensions; however, no clear trends are identifiable. Comparisons of test data for the honeycomb seals with labyrinth and smooth annular seals shows the honeycomb seal had the best sealing (minimum leakage) performance, followed in order by the labyrinth and smooth seals. For prerotated fluids entering the seal, in the direction of shaft rotation, the honeycomb seal has the best rotordynamic stability followed in order by the labyrinth and smooth. For no prerotation, or fluid prerotation against shaft rotation, the labyrinth seal has the best rotordynamic stability followed in order by the smooth and honeycomb seals.

Segmentation Effects on Brush Seal Leakage and Rotordynamic Coefficients

2015 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Manuel Gaszner ◽  
Christos Georgakis ◽  
Paul Cooper
Keyword(s):  
Electrical Discharge ◽  
Electrical Discharge Machining ◽  
Labyrinth Seal ◽  
Performance Characteristics ◽  
Radial Clearance ◽  
Single Plane ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Stiffness And Damping

This paper studies the effect of brush seal segmentation on the seal performance characteristics. A brush-labyrinth sealing configuration arranged of one brush seal downstream and two labyrinth fins upstream is studied experimentally and theoretically. The studied brush seal is of welded design installed with zero cold radial clearance. The brush seal front and back rings as well as the bristle pack are segmented radially in a single plane using the electrical discharge machining technique. The segmentation procedure results in loss of bristles at the site of the cuts altering the leakage flow structure in the seal and its performance characteristics. Two test rigs are used to obtain leakage, as well as rotordynamic stiffness and damping coefficients of the seal at different pressure ratios. The CFD-based model is used to predict the seal performance and to study in detail local changes in the flow field due to the segmentation. A back-to-back comparison of the performance of non-segmented and segmented brush seals, as well as baseline labyrinth seal is provided. The obtained results demonstrate that the segmentation in general negatively affects the performance of the studied brush-labyrinth sealing configuration. However, the segmented brush seal shows increased direct damping coefficients.

Influence of Groove Size on the Static and Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals

2007 ◽  
Vol 129 (2) ◽  
pp. 398-406 ◽  
Author(s):  
Dara W. Childs ◽  
Matthew Graviss ◽  
Luis E. Rodriguez
Keyword(s):  
Energy Equation ◽  
Groove Depth ◽  
Added Mass ◽  
Equation Model ◽  
Radial Clearance ◽  
Pressure Perturbation ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Test Conditions ◽  
Groove Test

Test results are presented for a smooth seal and three centrally grooved seals that are representative of buffered-flow oil seals in centrifugal compressors. The seals are short (L∕D≅0.21), with a diameter of 117mm and a nominal radial clearance of 0.085mm, netting the clearance-to-radius ratio 0.0015. The grooves have groove depth to clearance ratios (Dg∕Cr) of 5, 10, and 15. Test conditions include three shaft speeds from 4000rpm to 10,000rpm, three inlet oil pressures from 24bar to 70bar, and seal eccentricity ratios from 0 (centered) to 0.7. Dynamic results include stiffness, damping, and added-mass coefficients; static results include stator position, attitude angles, and seal leakage. Stiffness, damping, and mass coefficients plus leakage are compared for the seal geometries. Results show that all rotordynamic coefficients consistently decrease with increasing seal groove depths, and seal leakage is largely unchanged. Comparisons are also made between experimental results and predictions from a computer program based on a Reynolds + energy equation model. The model includes the assumption that a groove is large enough to create separate lands within the seal, creating a zero or negligible pressure perturbation within the groove. Test results show that even the deepest groove depth tested is not deep enough to satisfy this assumption.

Leakage and Rotordynamic Coefficients of Brush Seals With Zero Cold Clearance Used in an Arrangement With Labyrinth Fins

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Manuel Gaszner ◽  
Alexander O. Pugachev ◽  
Christos Georgakis ◽  
Paul Cooper
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Dynamic Test ◽  
Radial Clearance ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Brush Seal ◽  
Stiffness And Damping

A brush-labyrinth sealing configuration consisting of two labyrinth fins upstream and one brush seal downstream is studied experimentally and theoretically. Two slightly different brush seal designs with zero cold radial clearance are considered. The sealing configurations are tested on the no-whirl and dynamic test rigs to obtain leakage performance and rotordynamic stiffness and damping coefficients. The no-whirl tests allow identification of the local rotordynamic direct and cross-coupled stiffness coefficients for a wide range of operating conditions, while the dynamic test rig is used to obtain both global stiffness and damping coefficients but for a narrower operating range limited by the capabilities of a magnetic actuator. Modeling of the brush-labyrinth seals is performed using computational fluid dynamics. The experimental global rotordynamic coefficients consist of an aerodynamic component due to the gas flow and a mechanical component due to the contact between the bristle tips and rotor surface. The computational fluid dynamics (CFD)–based calculations of rotordynamic coefficients provide, however, only the aerodynamic component. A simple mechanical model is used to estimate the theoretical value of the mechanical stiffness of the bristle pack during the contact. The results obtained for the sealing configurations with zero cold radial clearance brush seals are compared with available data on three-tooth-on-stator labyrinth seals and a brush seal with positive cold radial clearance. Results show that the sealing arrangement with a line-on-line welded brush seal has the best performance overall with the lowest leakage and cross-coupled stiffness. The predictions are generally in agreement with the measurements for leakage and stiffness coefficients. The seal-damping capability is noticeably underpredicted.

Measurement Versus Predictions of Rotordynamic Coefficients of a Hole-Pattern Gas Seal With Negative Preswirl

2012 ◽  
Author(s):  
Philip D. Brown ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
Ideal Gas ◽  
Rotor Speed ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
The Cross ◽  
Gas Seals ◽  
Stiffness And Damping

Test results are presented for rotordynamic coefficients of a hole-pattern annular gas seals at supply pressures to 84 bar and running speeds to 20,200 RPM. The principal test variable of interest was negative preswirl. Preswirl signifies the circumferential fluid flow entering a seal, and negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation. The influences of pressure ratio and rotor speed were also investigated. Measured results produce direct and cross-coupled stiffness and damping coefficients that are a function of excitation frequency Ω. Changes in pressure ratio had only small effects on most rotordynamic coefficients. Cross-coupled stiffness showed slightly different profiles through the mid-range of Ω values. Increasing rotor speed significantly increased cross-coupled stiffness and cross-coupled damping. At 10,200 RPM, high negative inlet preswirl produced negative cross-coupled stiffness over an excitation frequency range of 200–250 Hz. Negative preswirl did not affect direct stiffness and damping coefficients. Effective damping combines the stabilizing effect of direct damping and the destabilizing effect of cross-coupled stiffness. The cross-over frequency is the precession frequency where effective damping transitions from a negative value to a positive value with increasing frequency. At 20,200 RPM with a pressure ratio of 50%, peak effective damping was increased by 50%, and the cross-over frequency was reduced by 50% for high-negative preswirl versus zero preswirl. Hence, reverse swirl can greatly enhance the stabilizing capacity of hole-pattern balance-piston or division-wall seals for compressors. A two-control-volume model that uses the ideal gas law at constant temperature was used to predict rotordynamic coefficients. The model predicted direct rotordynamic coefficients well, but substantially under predicted cross-coupled rotordynamic coefficients especially at high negative preswirls.

Static Performance Characteristics and Rotordynamic Coefficients for a Four-Pad Ball-in-Socket Tilting Pad Journal Bearing

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Dara Childs ◽  
Joel Harris
Keyword(s):  
Power Loss ◽  
Journal Bearing ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Test Conditions ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Static Performance ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Static performance characteristics and rotordynamic coefficients were experimentally determined for a four-pad, ball-in-socket, tilting-pad journal bearing in load-between-pad configuration. Measured static characteristics include journal static equilibrium position, estimated power loss, and trailing-edge pad temperatures. Rotordynamic coefficients were determined from curve-fits of measured complex dynamic-stiffness coefficients as a function of the excitation frequency. Aside from the cross-coupled damping coefficients, a frequency-independent [M]-[C]-[K] model did a good job of fitting the measurements. The added-mass coefficient was frequently dropped, leaving only a frequency-independent stiffness and damping coefficient. Test conditions included speeds from 4000 rpm to 12,000 rpm and unit loads from 0 kPa to 1896 kPa (0–275 psi). The bearing uses cool inlet oil to decrease the pad operating temperatures and increase the bearing’s load and speed capacity. The bearing has a nominal radial clearance of 95.3 μm (3.75 mils). However, measurements indicated significant bearing crush with a radial bearing clearance of 99.6 μm (3.92 mils) in the axis 45 deg counterclockwise from the loaded axis and 54.6 μm (2.15 mils) in the axis 45 deg clockwise from the loaded axis (assuming counterclockwise rotation). The pad length is 101.60 mm (4.00 in.), giving L/D=1.00. The pad arc angle is 73 deg, and the pivot offset ratio is 65%. Testing was performed using a test rig described by Kaul (1999, “Design and Development of a Test Setup for the Experimental Determination of the Rotordynamic and Leakage Characteristics of Annular Bushing Oil Seals,” MS thesis, Texas A&M University, College Station, TX), and rotordynamic coefficients were extracted using a procedure adapted from the work of Childs and Hale (1994, “A Test Apparatus and Facility to Identify the Rotordynamic Coefficients of High-Speed Hydrostatic Bearings,” ASME J. Tribol., 116, pp. 337–344). A bulk-flow Navier–Stokes model was used for predictions, using adiabatic conditions for the fluid in the bearing. However, the model assumes constant nominal clearances at all pads, and an average clearance was used based on measured clearances. Measured static eccentricities and attitude angles were significantly higher than predicted. Attitude angles varied from 6 deg to 39 deg and decreased with load. Power loss was underpredicted at low speeds and very well predicted at high speeds, with a maximum value of 25 kW (34 hp). The maximum detected pad temperature was 71°C(160°F) while the temperature increase from inlet to maximum pad temperature location was overpredicted by 10–40%. Direct stiffness and damping coefficients were significantly overpredicted, but the addition of a stiffness-in-series correction vastly improved the agreement between theory and experiment. Direct added masses were zero or negative at low speeds and increased with speed up to a maximum of about 50 kg; they were normally greater in the x (unloaded) direction. Although significant cross-coupled stiffness terms were present, they always had the same sign, and the bearing had a whirl frequency ratio of zero netting unconditional stability over all test conditions.

Rotordynamic Characteristics of a Flexure Pivot Pad Bearing With an Active and Locked Integral Squeeze Film Damper

2012 ◽  
Author(s):  
Jeff Agnew ◽  
Dara Childs
Keyword(s):  
Added Mass ◽  
Squeeze Film ◽  
Test Results ◽  
Squeeze Film Damper ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Active Damper ◽  
Rotordynamic Coefficient

Measured rotordynamic coefficients are presented for a flexure-pivot-pad journal bearing (FPJB) in a load-between-pad configuration with: (1) an active, and (2) locked integral squeeze film damper (ISFD). Prior rotordynamic-coefficient test results have been presented for FPJBs (alone), and rotor-response results have been presented for rotors supported by FPJBS with ISFDs; however, these are the first rotordynamic-coefficient test results for FPJBs with ISFDs. A multi-frequency dynamic testing regime is employed. For both bearing configurations, quadratic curve fits provide good representation of the real portions of the dynamic-stiffness coefficients yielding a direct stiffness and a direct added-mass coefficient. The imaginary portions are well represented by linear curve fits, implying constant, frequency-independent direct-damping coefficients. Direct stiffness coefficients are ∼50% lower for the active-damper configuration, and direct damping coefficients are only modestly lower. The combination of ∼50% reduction in direct stiffness with a modest drop in direct damping indicates a very effective squeeze-film damper application. Added-mass coefficients are normally lower for the active-damper configuration, and all coefficient trends (for changes in loading and shaft speed) are “flatter” for the active flexure pivot-pad damper bearing. The measured rotordynamic coefficients are used to calculate the whirl frequency ratio and indicate high stability for both bearing configurations.

The Rotordynamic Coefficients of Mechanical Seals Having Two Flexibly Mounted Rotors

1991 ◽  
Vol 113 (4) ◽  
pp. 795-804 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Mechanical Seal ◽  
Mechanical Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Rotating Shafts ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom ◽  
Degenerate Cases

The Reynolds equation is derived for a mechanical seal in which both elements are flexibly mounted to rotating shafts. Stiffness and damping coefficients for the fluid film are calculated for the three degrees of freedom of each element based upon a small perturbation analysis. The analogous coefficients for simpler configurations (e.g., flexibly mounted rotor, flexibly mounted stator) contained in the literature are shown to be obtainable as degenerate cases of the more general results presented in this work.

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